The investigators' hypotheses are (1) that prazosin will be more effective than placebo in easing the effects of chronic PTHAs, including headache frequency, duration, severity, use of abortive/analgesic medications, and disability caused, and (2) that improvement in headache parameters will be associated with improvement in sleep quality, PTSD symptom severity, mood, cognition, health-related quality of life, and global clinical status, and with moderation of alcohol consumption.